There are summer concerts in the ancient theater of Kourion on Cyprus. Weather wise, April could count as summer although the locals don't think so and my recollection is that the Kourion concerts don't start until later in the season. It's a great venue but I have no idea who handles the bookings. Nor do I recall ever seeing a nonlocal folk concert there. Some of the hotels around Paphos offer music during the seson (which begins around Easter), but again it is mostly local (i.e. Greek-style) music with bookings arranged through the individual hotels.

Well, that was no help...but it was fun to conjure up memories of that beautiful island. So thanks and have a great trip.